A pearl is formed when a foreign object gets into the mantle of a mollusk.
This irritation becomes covered with successive layers of nacre, which is the mother of pearl, and eventually forms a pearl.
Cultured pearls are probably easier to match, but natural pearls are more valuable.
For the cultured variety, pearl farmers keep the special oysters in confinement.
Foreign objects are purposefully entered into the mantle and the process of encystation begins and eventually many layers of nacre form a pearl.
This pearl can be harvested and a new irritant is placed in the mantle. This can be continued for the life of the mollusk.
Natural pearls are found in the pearl oysters, which are found in tropical seas, mostly in Asia.
Quite a large number would have to be found to be able to make a matched string, which would explain their greater value.
Freshwater pearls are just that. They are formed in the pearl mussels which are found in many rivers of Asia, Europe and the United States.
They, too, can be cultivated in pearl farms, and can be matched or not.